Question

How do you find the line that is perpendicular to `y=2/3x+1` and passes through (0, 5)?

Answer 1

`y=-3/2x+5`

Explanation:

Perpendicular lines have opposite reciprocal slope, `m`, in an equation. Meaning, if the slope of a line is a positive fraction, its reciprocal slope would be negative.

The given equation is a linear equation, `y=mx+b`

Where `m` is the slope, `(rise)/(run`, and `b` is the y intercept

To find a line that is perpendicular to the given equation, use the opposite reciprocal slope and point and solve using the point-slope formula

`y-y_1=m(x-x_1)`

`m=-3/2`

`y_1=5`

`x_1=0`

`y-5=-3/2(x-0)`

Distribute the `-3/2` throughout the set of parenthesis

`y-5=-3/2x+0`

Add `5` on both sides of the equation

`y=-3/2x+5`

And now you can see the slope is the opposite reciprocal of the original equation

Answer 2

`y = -3/2x+5`

Explanation:

If lines are perpendicular, one slope is the negative reciprocal of the other.
(Their product is -1)

If `m_1 = 2/3," " m_2 = -3/2`

So we have the slope of the line perpendicular to the one given.

The point `(0,5)` is the y-intercept because the x-value is 0.
This is also known as 'c' `rarr c = 5`

The equation of a line is `y = mx +c`.
We have `m and c`

`y = -3/2x+5`